Nonlinear steering criteria for arbitrary two-qubit quantum systems

By employing Pauli measurements, we present some nonlinear steering criteria applicable for arbitrary two-qubit quantum systems and optimized ones for symmetric quantum states. These criteria provide sufficient conditions to witness steering, which can recover the previous elegant results for some well-known states. Compared with the existing linear steering criterion and entropic criterion, ours can certify more steerable states without selecting measurement settings or correlation weights, which can also be used to verify entanglement as all steerable quantum states are entangled.

[1]  M. Horodecki,et al.  Quantum entanglement , 2007, quant-ph/0702225.

[2]  M. Reid.  Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities , 2013, 1402.4235.

[3]  S. Wehner,et al.  Bell Nonlocality , 2013, 1303.2849.

[4]  Gerardo Adesso,et al.  Unconditional security of entanglement-based continuous-variable quantum secret sharing , 2016, 1603.03224.

[5]  Sabine Wollmann,et al.  Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering. , 2015, Physical review letters.

[6]  N. Brunner,et al.  One-way Einstein-Podolsky-Rosen Steering , 2014, 1402.3607.

[7]  Nathan Walk,et al.  Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution , 2014, 1405.6593.

[8]  V. Scarani,et al.  One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering , 2011, 1109.1435.

[9]  E. Schrödinger.  Probability relations between separated systems , 1936, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  A C Doherty,et al.  Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. , 2007, Physical review letters.

[11]  Zeng-Bing Chen,et al.  Certifying Einstein-Podolsky-Rosen steering via the local uncertainty principle , 2016 .

[12]  Entanglement and permutational symmetry. , 2008, Physical review letters.

[13]  A. C. Doherty,et al.  Entanglement, einstein-podolsky-rosen correlations, bell nonlocality, and steering , 2007, 0709.0390.

[14]  John Watrous,et al.  Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements , 2014, 1406.0530.

[15]  Jaehak Lee,et al.  Steering criteria via covariance matrices of local observables in arbitrary-dimensional quantum systems , 2015, 1509.02550.

[16]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

[17]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[18]  S. Woods,et al.  The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. S. 211-215 , 2005 .

[19]  R. Werner,et al.  Observation of one-way Einstein–Podolsky–Rosen steering , 2012, Nature Photonics.

[20]  D. J. Saunders,et al.  Experimental EPR-steering using Bell-local states , 2009, 0909.0805.

[21]  C. H. Oh,et al.  All entangled pure states violate a single Bell's inequality. , 2012, Physical review letters.

[22]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[23]  I. Jolliffe.  Principal Component Analysis , 2002 .

[24]  Gerardo Adesso,et al.  Secure Continuous Variable Teleportation and Einstein-Podolsky-Rosen Steering. , 2014, Physical review letters.

[25]  Hideo Mabuchi,et al.  Characterizing the entanglement of symmetric many-particle spin-1/2 systems , 2003 .

[26]  Eric G. Cavalcanti,et al.  Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations , 2013, 1303.7432.

[27]  R. Werner,et al.  Entanglement measures under symmetry , 2000, quant-ph/0010095.

[28]  N. Gisin.  Hidden quantum nonlocality revealed by local filters , 1996 .

[29]  David J. Gross,et al.  Symmetry in Physics: Wigner's Legacy , 1995 .

[30]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .